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Question
Calculate the correlation coefficient from the data given below:
| X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Y | 9 | 8 | 10 | 12 | 11 | 13 | 14 | 16 | 15 |
Solution
| X | Y | x = X − 5 | y = Y − 12 | x2 | y2 | xy |
| 1 | 9 | − 4 | − 3 | 16 | 9 | 12 |
| 2 | 8 | − 3 | − 4 | 9 | 16 | 12 |
| 3 | 10 | − 2 | − 2 | 4 | 4 | 4 |
| 4 | 12 | − 1 | 0 | 1 | 0 | 0 |
| 5 | 11 | 0 | − 1 | 0 | 1 | 0 |
| 6 | 13 | 1 | 1 | 1 | 1 | 1 |
| 7 | 14 | 2 | 2 | 4 | 4 | 4 |
| 8 | 16 | 3 | 4 | 9 | 16 | 12 |
| 9 | 15 | 4 | 3 | 16 | 9 | 12 |
| 45 | 108 | 0 | 0 | 60 | 60 | 57 |
Correlation coefficient
r(x, y) = `(sum"xy")/(sqrt (sum"x"^2) xx sqrt (sum"y"^2))`
= `57/(sqrt60 xx sqrt(60))`
= `57/60`
r = 0.95
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